Eisenstein Hecke algebras and conjectures in Iwasawa theory

Wake, Preston

doi:10.2140/ant.2015.9.53

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Cited by 2 publications

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“…But by the previous lemma, Fitt Λ (I/I 2 ) ⊂ (ξ) = char Λ (X χ (1)). This implies that the ker(Θ) is finite (see [Wak15a,Lem. A.7] for example), and hence ker(Θ) = 0, since X χ (1) has no finite submodule by Ferrero-Washington [FW79].…”

Section: Lemma 422 Let a Be A Ring Let M Be A Finitely Presented mentioning

confidence: 99%

Ordinary pseudorepresentations and modular forms

Wake

Wang-Erickson

2017

Proc. Amer. Math. Soc. Ser. B

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Abstract. In this note, we observe that the techniques of our paper "Pseudomodularity and Iwasawa theory" can be used to provide a new proof of some of the residually reducible modularity lifting results of Skinner and Wiles. In these cases, we have found that a deformation ring of ordinary pseudorepresentations is equal to the Eisenstein local component of a Hida Hecke algebra. We also show that Vandiver's conjecture implies Sharifi's conjecture.

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Section: Lemma 422 Let a Be A Ring Let M Be A Finitely Presented mentioning

confidence: 99%